Six more than three times a number is less than or equal to 96.

Answers

Answer 1

Answer: 3x+6≤96
three x plus six is less than or equal to 96.

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Solve each system by the addition method.-4x+7y =9
2y=-5x-22
Put the answer in (x,y) form

Answers

-4x + 7y = 9 ⇒ -4x + 7y = 9 ⇒    8x - 14y = -18
2y = -5x - 22 ⇒ -5x - 2y = 22 ⇒ -35x - 14y = 154
       43x = -172
      43    43
   x = -4
      -4x + 7y = 9
         -4(-4) + 7y = 9
      16 + 7y = 9
      - 16     - 16
      7y = -7
   7 7
      y = -1
      (x, y) = (-4, -1)

Un topografo situado en un punto c localiza dos puntos a y b en los lados opuestos de un lago . Si el punto c esta situado a 5km de a y 8 km de b y ademas el angulo formado en el punto c es de 36 grados . Calcular el ancho del lago

Answers

The width of the lake is approximately 4.93 kilometers.

To calculate the width of the lake, you can use trigonometry. You have a triangle with one side of 5 km (from point C to point A), another side of 8 km (from point C to point B), and an included angle of 36 degrees at point C.

You can use the law of cosines to find the third side, which is the width of the lake (let's call it "x"). The law of cosines states:

$c^2 = a^2 + b^2 - 2ab * cos(C)$

Where:

c is the side you want to find (the width of the lake, in this case).

a is the side opposite to angle A (5 km).

b is the side opposite to angle B (8 km).

C is the included angle at point C (36 degrees).

So, plug in the values:

$x^2 = 5^2 + 8^2 - 2 * 5 * 8 * cos$ (36 degrees)

Now, you can solve for x:

$x^2 = 25 + 64 - 80 * cos$ (36 degrees)

$x^2 = 89 - 80 * cos$ (36 degrees)

Now, you'll need to calculate the cosine of 36 degrees, which is approximately 0.809.

$x^2 = 89 - 80 * 0.809\nx^2 = 89 - 64.72\nx^2 = 24.28$

Now, take the square root of both sides to find the width of the lake:

x ≈ √24.28

x ≈ 4.93 km

So, the width of the lake is approximately 4.93 kilometers.

for such more question on triangle

brainly.com/question/1058720

#SPJ2

Hi mods, I do have a link in this answer but it is a link to the spanish version of brainly since this user seems to speak spanish.

Por favor, traduzca su pregunta al inglés o encuentre la versión en español de Brainly (https://brainly.com.br/ o https://brainly.lat/.)

Estoy usando el traductor de google, lo siento por el mal español

ver diagrama adjunto abajo (el asombrosamente dibujado)

podemos formar un triangulo

Usa la ley de los cosenos del segundo apego.

Queremos encontrar el valor de c que representa el ancho del lago

En este problema, a=5, b=8, y C=36°

$c^2=a^2+b^2-2abcos(C)$

$c=√(a^2+b^2-2abcos(C))$

$c=√(5^2+8^2-2(5)(8)cos(36^o))$

$c=√(25+64-80cos(36^o))$

$c=√(89-80cos(36^o))$

c≈4.92734 km

el ancho del lago es de aproximadamente 4.93km

The scale diagram of a basketball court uses a scale of 1:280. The length of the court measures 10 cm in the diagram the actual length of the court is ______________ meters (round to the nearest meter)

Answers

10*280=2800 centimeters
2800 centimeters=28 meters
28 meters

A certain been plant grows 15% in height each day. Today after 10 days it is 27 inches tall. How tall was it yesterday?

Answers

$x+0.15x=27\n 1.15x=27\n x\approx23.48\hbox{ in}$

At a fundraiser breakfast, the bill for three glasses of orange juice and five pancake specials is $7.60, whereas the bill for one glass of orange juice and two pancake specials is $2.90. The system of equation {(3j 5p=7.60@j 2p=2.90)┤ represents this situation, where j represents the cost of a glass of orange juice and p represents the cost of a pancake special. What would be the bill for one glass of orange juice and one pancake special?

Answers

Ok, so you are looking for the price of the orange juice and the pancake special individually. So, the first step is to declare our variables:

j = price of the orange juice.
p = price of the pancake special.

So the first bill, translated with our variables is
3j + 5p = 7.60

The second bill, translated with our variables is
1j + 2p = 2.90

Now, it says to use the substitution method, so we need to solve one of those equations for one variable. Since in the second equation, we have one term with a coefficient of 1, that will be the easiest to solve for. So we move everything other than that term to the other side.

1j = 2.90 - 2p

Now we have j solved for, we will substitute it into the other equation

3(2.90 - 2p) + 5p = 7.60

Now we have only one variable, so we just simplify

8.70 - 6p + 5p = 7.60
-1p = -1.10
p = 1.10

Now we know how much the pancake special costs, we can plug this into either of the two original equations and solve for the price of the orange juice.

1j + 2(1.10) = 2.90
j = 0.70

Now part c asks for the cost of one orange juice and one pancake special. So, with our variables, that will be:
j + p

We already know the values of these variables, so we can plug them in.

0.70 + 1.10 = $1.80

2) Linear combination is the same as the addition/elimination method. This means your goal is to add the equations together. But before we do that, we want to multiply one row by some random number so that when we add the rows together, we can get rid of one of the variables.

a - 2b = 2
a - 1b = 6

So we have two choices here. We can multiply one of the a's by -1 to make it negative. That way one of them is positive, and the other is negative, and they will cancel when we add them together. OR we can multiply the bottom equation by -2. This will make the b variable in the bottom row a +2b and it will cancel out with the -2b in the top equation.

Both will give you the right answer, so it won't matter which way you go. Since it's a smaller number, I'm going to go with the first way, and multiply the top a by -1.

Note: You need to multiply EVERYTHING in the equation by the number!

-1(1a - 2b = 2)
a - b = 6

-a + 2b = -2
a - b = 6

When you add the rows together, simply add like terms. Notice the a will cancel out. The +2b will add with the -b to make 1b and the -2 will add with the 6 to make 4

So we have:

1b = 4

And now we can go back up and plug this info in to solve for the other variable

a - (4) = 6
a = 10

We have a system of equation:
3j + 5p= $7.60 (1)
j + 2p= $2.90 (2)

Multiply equation (2) by 3:
3j + 6p = $8.70 (3)

Take (3)- (1), we have:
(3j) - (3j) + (6p - 5p) = $8.70- $7.60
⇒ p= $1.10

Now, we use equation (2) to find j:
j= $2.90- 2* $1.10
⇒ j= $0.70

j+ p= $0.70 + $1.10= $1.80

The bill for one glass of orange juice and one pancake special would be $1.80.

Hope this helps~

The table below shows the amount of money, in hundreds of dollars, Elliot has saved after different numbers of years: Identify the function that represents Elliot's savings and the amount that Elliot will have saved in 9 years.

y = 15x, in 9 years he will have saved $13,500
y = x + 15, in 9 years he will have saved $2,400
y = 6x, in 9 years he will have saved $5,400
y = x + 90, in 9 years he will have saved $9,900

Answers

Table:
Years (x) 1 2 3 4 5 6
Money (y) (hundreds of dollars) 15 30 45 60 75 90

y = 15(x)
y = 15(9)
y = 135 hundreds of dollars

y = 15x, in 9 years he will have saved $13,500

Answer:it’s a, 13,500. I took the test

Step-by-step explanation:

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